# Homework Help: How many rotations of peddels per second?

1. Oct 10, 2009

1. The problem statement, all variables and given/known data
A bicycle drives on a straight road with a velocity v = 18 km/h. How many turns (rotations) of peddles per second must be carried out by cyclists, if the radius of the wheels r = 35 cm, and the ratio of the radii of front and rear gear wheels is 2:1?

2. Relevant equations

I used formula v=2(pi)r * f

3. The attempt at a solutionSo, I have another problem which says:

I converted: 18km/h = 5m/s and 35cm = 0.35m, so now we have all units unified.

I plugged the numbers into the formula and got the result f= 2.27.

And now we have the ratio 2:1, and since the the front gear wheel is larger than the rear one I multiplied by 2 and got the FINAL result which is 4.55 turns of peddles per second.
Are my calculations correct?
Thank you for all the help!

2. Oct 10, 2009

### mgb_phys

If the ratio of the gears is 2:1 doesn't that mean 2revs of the pedals to each rotation of the rear wheel?

3. Oct 11, 2009

So that mean that I have to divide by to and the correct final answer is f= 1.14?

4. Oct 11, 2009

### mgb_phys

Yes -
Twice the radaii on the front cog means that it rotates once for 2 rotations of the back cog (and hence the back wheel) - this is the normal gearing for a bike (except the lowest gear on a mountain bike) - I thought the question had claimed the opposite.

5. Oct 11, 2009